Playing mixed strategies with Leo Messi

Playing a mixed strategy means in game theory choosing a probability distribution between two or more available actions (or pure strategies). For example, tossing a coin to decide whether to kick to the left or to the right, is one possible choice of a mixed strategy. In the real world, we don’t take many decisions literally like this. But some interactions have been found were actors decide as if choosing mixed strategies. One that is easily amenable to empirical work is penalty kicks in soccer. Economist Palacios-Huerta and psychologist Bar-Eli, separately, have found that both kickers and goal-keepers behave as if choosing rationally their mixed strategies (not literally, because they do not toss coins or other random devices, but mentally, intuitively).

As a result of Leo Messi missing a few important penalties recently, there is a debate about his suitability to the job of kicking penalties. But data shows that he behaves optimally, as predicted by scholars: mostly shooting to his natural side, sometimes to the other, missing around 20% of penalties and achieving a similar success ratio when kicking to the right or to the left (otherwise there would be one clear best strategy, and he would be predictable). That means that he is probably rational and optimal.

It s also true that he may illustrate another feature uncovered by behavioural sciences: choking under pressure. His success ratio decreases dramatically when he kicks crucial penalties (at the end of games most notably).

Messi is an average penalty kicker. Should he be replaced in that role? Probably if another player kicked the same number of penalties he would also score around 80% like Messi, although perhaps doing better in the last minutes of games. But no manager in the world will tell the best player not to kick a penalty if he wishes. Should he think more about how to kick penalties? Should he have a penalty coach, a full time employee working on that with him? That would interfere with his natural decision making process, which is intuitive and unconscious. That is his way of being rational.

I was almost wrong in November 2013 when I wrote a post suggesting to sell Messi (well, just playing with the idea): he did better in the World Cup with Argentina than I expected (although as I expected Argentina did not win, and his winning the trophy to the best player was controversial), and this season he is in much better shape so far than I expected (better than in the World Cup). But does that mean that I am not wrong or that I am still right? That is, perhaps since he is still so valuable it is still time to sell him NOW because a lot of money can be made that can be used to maximize the long run probability of winning games and titles. He is better than I expected, but he is not better than he was in 2008-2011, and he will not get much better than that (in other words, he is beyond his peak age). In penalty kicks he is certainly not better.

Since there is no clear option about selling him or not, perhaps the best way to decide about that is to randomize. And perhaps that is precisely what FC Barcelona are doing by replacing technical director Andoni Zubizarreta by a bicephalous body with the heads of two unpredictable agents: veteran former player Carles Rexach and former Berlusconi employee in AC Milan Ariedo Braida.